How to demand a court of record ?

By the phrase you used it sounds like you want to appeal your case. I strongly advise you to talk to an attorney about doing so. Getting a copy of the transcripts of the case varies based on county, but it's usually just a matter of asking the clerk of court for a copy. You will likely have to pay a fee as well.

Submitting a letter to the court won't help. There is not enough information in your question to give you a proper answer. www.BryceFetter.com

Purely a guess. Are you trying to demand a jury trial ?